Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.



Figure 7.

Figure 8.

Figure 9.

Figure 10.


Figure 11.

Figure 12.

Figure 13.

Figure 14.

Figure 15.

Figure 16.

Figure 17.

Figure 18.

Figure 19.

Figure 20.

Figure 21.

Figure 22.

Comparison of different dynamic path planning algorithms across different scenarios
| Map Type | Case | Path Length | Time | Turning Radius | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
| D-TIG | APF | APPATT | D-TIG | APF | APPATT | D-TIG | APF | APPATT | ||
| Short | C17 | 520.46 | 844.00 | 519.67 | 0.03 | 0.11 | 0.04 | 1.72 | 35.01 | 2.22 |
| C18 | 485.87 | 718.00 | 491.07 | 0.03 | 0.08 | 0.03 | 0.64 | 147.98 | 3.45 | |
| C19 | 509.74 | 531.00 | 510.58 | 0.01 | 0.07 | 0.01 | 0.82 | 63.21 | 1.57 | |
| C20 | 625.68 | 885.00 | N/A | 0.04 | 0.12 | N/A | 3.08 | 13.03 | N/A | |
| Large | C21 | 1010.41 | 1406.00 | 1010.01 | 0.07 | 0.14 | 0.05 | 1.38 | 10.65 | 1.90 |
| C22 | 1125.06 | 1419.00 | 1124.14 | 0.06 | 0.14 | 0.04 | 1.99 | 9.66 | 2.28 | |
| C23 | 1036.91 | 1401.00 | 1033.27 | 0.04 | 0.14 | 0.03 | 3.52 | 1200.42 | 2.86 | |
| C24 | 990.64 | N/A | 994.53 | 0.03 | N/A | 0.04 | 1.95 | N/A | 3.40 | |
| Sparse | C25 | 495.73 | 687.00 | 496.27 | 0.02 | 0.06 | 0.01 | 1.08 | 7.26 | 1.65 |
| C26 | 516.49 | 532.00 | 518.80 | 0.01 | 0.04 | 0.01 | 1.08 | 2.98 | 2.17 | |
| C27 | 489.01 | 552.00 | 489.39 | 0.01 | 0.05 | 0.01 | 0.63 | 184.25 | 1.18 | |
| C28 | 508.54 | 536.00 | 513.59 | 0.01 | 0.05 | 0.01 | 2.21 | 8.04 | 3.59 | |
| Dense | C29 | 558.54 | N/A | N/A | 0.05 | N/A | N/A | 6.51 | N/A | N/A |
| C30 | 562.17 | N/A | N/A | 0.06 | N/A | N/A | 5.92 | N/A | N/A | |
| C31 | 505.38 | N/A | 505.14 | 0.04 | N/A | 0.05 | 1.86 | N/A | 2.59 | |
| C32 | 564.15 | N/A | N/A | 0.06 | N/A | N/A | 7.55 | N/A | N/A | |
Comparison of Different Dynamic Path Planning Algorithms Across Different Scenarios
| Map Type | Case | Path Length | Time | Turning Radius | |||
|---|---|---|---|---|---|---|---|
| D-TIG | APPATT | D-TIG | APPATT | D-TIG | APPATT | ||
| Short | C17 | 520.46 | 571.56 | 0.02 | 0.03 | 0.55 | 4.12 |
| C18 | 496.99 | 502.81 | 0.01 | 0.01 | 1.62 | 1.36 | |
| C19 | 513.46 | 520.09 | 0.005 | 0.007 | 0.97 | 1.47 | |
| Large | C21 | 1017.12 | N/A | 0.02 | N/A | 2.03 | N/A |
| C22 | 1130.68 | 1244.94 | 0.08 | 0.01 | 1.56 | 4.44 | |
| C23 | 1027.61 | 1044.94 | 0.03 | 0.01 | 2.70 | 3.99 | |
| Sparse | C25 | 494.90 | 522.74 | 0.001 | 0.003 | 0.97 | 4.27 |
| C26 | 534.93 | N/A | 0.002 | N/A | 2.2 | N/A | |
| C27 | 495.09 | 561.69 | 0.008 | 0.002 | 1.48 | 4.42 | |
Comparison of different static path planning algorithms across four scenarios
| Map Type | Case | Path Length | Time | Turning Radius | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| S-TIG | A* | PRM | RRT | APPATT | TG | S-TIG | A* | PRM | RRT | APPATT | TG | S-TIG | A* | PRM | RRT | APPATT | TG | ||
| Short | C1 | 493.84 | 510.06 | 949.33 | 566.49 | 495.29 | 493.59 | 0.01 | 8.44 | 3.65 | 0.18 | 0.09 | 0.20 | 0.53 | 32.20 | 58.35 | 14.96 | 1.45 | 0.53 |
| C2 | 511.89 | 533.16 | 661.20 | 595.68 | N/A | 511.60 | 0.07 | 11.72 | 3.65 | 0.27 | N/A | 2.73 | 0.68 | 32.20 | 42.18 | 16.84 | N/A | 0.46 | |
| C3 | 520.53 | 545.25 | 587.87 | 931.31 | 531.38 | 514.25 | 0.06 | 9.26 | 3.68 | 0.64 | 0.21 | 2.81 | 2.81 | 49.48 | 30.59 | 36.17 | 1.99 | 1.86 | |
| C4 | 527.59 | 557.87 | 645.85 | 840.31 | 584.34 | 528.50 | 0.06 | 10.38 | 3.36 | 0.14 | 0.06 | 2.02 | 2.34 | 46.33 | 37.94 | 26.21 | 2.72 | 2.34 | |
| Large | C5 | 1063.13 | 1156.40 | 1071.65 | 1429.14 | 1135.71 | 1063.76 | 0.11 | 73.00 | 5.25 | 0.77 | 0.15 | 73.48 | 1.97 | 55.76 | 6.43 | 34.66 | 9.28 | 1.72 |
| C6 | 1004.27 | 1022.01 | 1040.68 | 1313.74 | 1064.00 | 1004.14 | 0.02 | 92.65 | 5.09 | 0.35 | 0.10 | 0.14 | 0.16 | 10.21 | 7.20 | 34.58 | 1.87 | 0.14 | |
| C7 | 1241.35 | 1289.83 | 1253.50 | 1558.46 | N/A | 1238.23 | 0.05 | 80.09 | 5.88 | 0.78 | N/A | 4.13 | 1.49 | 69.90 | 6.69 | 44.56 | N/A | 1.07 | |
| C8 | 1001.01 | 1054.11 | 1019.10 | 1254.34 | 1925.46 | 999.66 | 0.09 | 72.85 | 5.25 | 0.39 | 0.14 | 8.57 | 1.67 | 52.62 | 5.08 | 35.32 | 10.29 | 1.42 | |
| Sparse | C9 | 522.01 | 545.98 | 524.81 | 706.33 | 543.33 | 522.24 | 0.04 | 16.00 | 9.85 | 0.11 | 0.01 | 0.83 | 1.02 | 18.06 | 2.30 | 8.14 | 5.55 | 1.02 |
| C10 | 515.36 | 548.42 | 526.48 | 714.74 | 515.30 | 515.38 | 0.03 | 17.47 | 9.02 | 0.02 | 0.03 | 0.04 | 0.25 | 14.92 | 4.76 | 12.66 | 0.24 | 0.24 | |
| C11 | 514.74 | 524.83 | 525.51 | 643.16 | 524.88 | 514.81 | 0.01 | 12.82 | 9.44 | 0.11 | 0.05 | 0.03 | 0.37 | 13.35 | 6.32 | 16.09 | 0.69 | 0.37 | |
| C12 | 511.61 | 520.28 | 525.26 | 613.53 | N/A | 509.00 | 0.06 | 16.69 | 9.36 | 0.09 | N/A | 0.16 | 2.05 | 16.49 | 6.08 | 15.28 | N/A | 1.14 | |
| Dense | C13 | 601.13 | 652.94 | 613.57 | 713.55 | N/A | 602.23 | 0.32 | 6.71 | 10.90 | 0.34 | N/A | 57.50 | 2.97 | 69.90 | 9.38 | 17.87 | N/A | 2.96 |
| C14 | 509.77 | 562.94 | 515.49 | 604.97 | N/A | 509.69 | 0.29 | 6.73 | 9.25 | 0.47 | N/A | 5.26 | 2.46 | 62.05 | 6.15 | 12.70 | N/A | 2.14 | |
| C15 | 686.06 | 698.61 | 638.75 | 868.91 | N/A | 686.05 | 0.68 | 6.16 | 11.60 | 0.42 | N/A | 62.59 | 18.90 | 68.33 | 13.63 | 23.39 | N/A | 18.90 | |
| C16 | 572.76 | 644.14 | 574.83 | 711.90 | N/A | 568.13 | 0.32 | 4.35 | 10.10 | 0.34 | N/A | 61.27 | 11.80 | 52.62 | 7.33 | 17.47 | N/A | 3.80 | |
Definitions of main notations
| Notations | Description |
|---|---|
| S | Start-point |
| T | Target-point |
| w | A waypoint generated by the tangent planner |
| CurrentSet | A set to store candidate waypoints |
| ClosedSet | A set to store visited waypoints |
| treatedSet | A set that records tangent points that have already been calculated |
